About planetary gravity

That would suggest that on one side of the Earth gravity would push you down (if the earth is between you and the center of the universe) and on the other side, gravity would fling you out into space.

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No, because there's no center of the universe. The universe is effectively infinite and its expansion is uniform.

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Well, I was responding to RB Kandy's suggestion about gravity being the force of the universe expanding outward. I don't see how it is possible to have this force coming from inside the Earth if Kandy's postulation is correct.

So, let me see if I've got this straight? In the beginning, the universe was infinitely dense in an infinite space. That infinite space then expanded, leading to the level of density that we are now familiar with in the universe. But since space is infinite and always has been (even though infinity seems to be getting bigger), it means that there can be no center to it. Am I grasping the concept so far?

I've certainly never been able to wrap my head around the idea that the universe is really a 2-dimensional or 4-dimensional object and that the 3-dimensional space that we interact with on a day-to-day basis is merely an illusion. It seems to me like Occam's Razor would slice that one to shreds. The fundamental existence of 3-dimensional space as the only space with any practical applications in the universe in which we live seems undeniable.

I suppose, if I'm to interpret the balloon analogy correctly, what you're saying is that, if there is a center to the universe, the center exists in a 4th dimension that cannot be measured and that is the thing that is actually expanding, causing the rest of the universe to become more spread out without changing the actual infinity of it all. Is that right? So that would mean that all matter in the universe, particularly galaxies, is spreading out and away from each other in all directions at equal rates, right?

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You've pretty much got it. The annoying thing about being humans is that we really can't quite comprehend the existence of things beyond out 3-dimensional space. Things like, how can the universe be "expanding" if it's already infinite? What exactly does an infinite thing expand into? Even the balloon analogy is flawed because we can clearly see the balloon getting larger and expanding into the air around it.

It's the same reason we have a problem with the question "If God created the universe, then who created God?" We can't grasp concepts like "forever" or "infinity" because we ourselves live such finite existences. My brain is too small to comprehend such big things.

You've pretty much got it. The annoying thing about being humans is that we really can't quite comprehend the existence of things beyond out 3-dimensional space. Things like, how can the universe be "expanding" if it's already infinite? What exactly does an infinite thing expand into? Even the balloon analogy is flawed because we can clearly see the balloon getting larger and expanding into the air around it.

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Agreed. The balloon analogy does help me wrap my head around the idea of everything expanding away from each other at an equal rate without anything moving towards anything else. But at first, I did have trouble, just with the way it was phrased, understanding the point; i.e. that while the balloon is expanding, the center has nothing to do with the surface of the balloon.

It's the same reason we have a problem with the question "If God created the universe, then who created God?" We can't grasp concepts like "forever" or "infinity" because we ourselves live such finite existences. My brain is too small to comprehend such big things.

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Mentally, I tidy that up by defining God as the thing that predates all things, including the universe. God is the ultimate original source of all creation and anything that was itself created cannot be called "God." If "God" created the universe but something else created "God," the something else would be God, not this "God" named thing. I have no problem with the idea that there is some kind of universal constant that exists before, after, and separate from the universe as a sort of bedrock upon which all other things exist.

So, let me see if I've got this straight? In the beginning, the universe was infinitely dense in an infinite space. That infinite space then expanded, leading to the level of density that we are now familiar with in the universe. But since space is infinite and always has been (even though infinity seems to be getting bigger), it means that there can be no center to it. Am I grasping the concept so far?

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Close enough for a BBS post. There are plenty of books on the subject if you want to examine it further.

I've certainly never been able to wrap my head around the idea that the universe is really a 2-dimensional or 4-dimensional object and that the 3-dimensional space that we interact with on a day-to-day basis is merely an illusion.

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Well, that's not what I'm saying here; it's just often helpful to use 2-dimensional surfaces as analogies for 3-dimensional space, because it's easier for people to grasp a "Flatland" in 3D space than to grasp a 3D volume in a 4D hyperspace.

The fundamental existence of 3-dimensional space as the only space with any practical applications in the universe in which we live seems undeniable.

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Well, except that there must be at least one additional dimension, time. It's not space, it's spacetime.

And if there are higher dimensions, they certainly could influence how things work in 3D space. String theory proposes that the differences between particles and forces are influenced by how the strings they're made of vibrate in other dimensions, and that the reason gravity is such a weak force is that most of it "leaks" out into other dimensions. Although I'm becoming increasingly skeptical that string theory is right, since there's still no real way to test it and it's basically an abstract exercise without evidence.

I suppose, if I'm to interpret the balloon analogy correctly, what you're saying is that, if there is a center to the universe, the center exists in a 4th dimension that cannot be measured and that is the thing that is actually expanding, causing the rest of the universe to become more spread out without changing the actual infinity of it all. Is that right?

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Not necessarily. That's what would be the case if the universe were closed, as I said, but evidence suggests it's flat. Again, the balloon description is just an analogy; you're not supposed to treat every part of it as meaningful, just to focus on the particular aspect that the analogy is meant to get across. For instance, I'm not suggesting that galaxies are really microbes, or that some big kid inflated the universe. The balloon-surface analogy is just one relatable example of a type of expansion without a center. Another that's often used in talking about the universe's expansion is a loaf of raisin bread rising in the oven, with all the raisins moving apart from each other uniformly. Of course in that case there's a center to the loaf of bread because it's finite in size, but the bread isn't expanding outward from that center point; rather, every part of it is getting farther away from every other part uniformly, discounting edge effects. If the loaf of bread were infinitely large, or at least larger than your ability to measure, you could not find a unique point that everything was expanding outward from, because every point within it fits that description equally well. The reason no point is the center of the universe is because every point is.

Suppose the universe were closed, but still edgeless? What if the universe as we perceive it were really the 4th dimensional equivalent of a sphere? If you travelled forever along its 3-dimensional "surface," you'd never reach the edge, although you might eventually come back to the point from which you started.

Do you have an equation for that "any freefall trip through the Earth would take only 42 minutes" thing? My dad kept insisting that the Fall couldn't work by freefall because the fastest speed you could possibly reach would be 150 miles per hour, which would mean the trip would take about 53 hours.

Do you have an equation for that "any freefall trip through the Earth would take only 42 minutes" thing? My dad kept insisting that the Fall couldn't work by freefall because the fastest speed you could possibly reach would be 150 miles per hour, which would mean the trip would take about 53 hours.

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Gardner didn't offer any specific equations in his article, I'm afraid. But your father must've been thinking of terminal velocity, the maximum allowed by air friction. The scenario Martin Gardner described in his essay assumed the tube was in vacuum and the train/elevator was magnetically suspended apart from the walls, so there was no friction and no terminal velocity limit.

Also, terminal velocity would be different depending on the density and surface area of the object and the density of the air it falls through (which is why a sheet of paper falls faster when crumpled than when flat). The 150 mph figure is terminal velocity for a human adult falling under 1g acceleration through the lower atmosphere of Earth, not a large elevator car. So if the car in the Fall wasn't in vacuum, there would be a terminal velocity, but we don't know what the actual value of it would be.

No, we just take as a postulate that the system of thought that establishes the existence of plurals can't itself be plural because it results in an inifinite recursion and what's known as the British English paradox, whereby they commit pluralization errors that are actually correct, which can't be true becaus they're also errors (thus the paradox).